Indian Syllogism

[Richard P. Hayes]

On Wed, 2006-03-08 at 13:33 +0100, Plamen Gradinarov wrote:

> I believe the way we arrive at the universal (and apodictic) character
> of the invariable concomitance (vyapti) has nothing to do with the
> Indian inferential mechanism

It could be argued that the use of positive and negative examples is to
give a precedent for seeing an instance of the pakṣa with an instance of
the hetu, and to give a precedence for seeing both absent at the same
time and the same place. The presence of the examples, if it has any
purpose at all, seems to be to give a basis for believing that there is
a vyāpti. The proposition that there is a vyāpti is synthetic, not
analytic.

When unpacks the full implications of anvaya and vyatireka, it amounts
to saying "In every instance observed so far, the hetu has been present
only when the pakṣa has not been absent." This leaves open the
possibility, as Peter observed, that future observations may well
deviate from the past. It is not part of the very definition of smoke
that it is accompanied by fire; it has simply been observed so far that
smoky loci and also fiery. This makes the inferential schema one that
yields high probability but not certainty. So the inference schema is
much like Hume's famous example of the sun rising tomorrow; it is by no
means certain that the sun will rise tomorrow, but that the sun will
probably rise tomorrow is how the smart money bets.

There are, of courses, cases cited in Indian philosophy of lines of
reasoning that involve analytic claims. We have the famous example of
the barren woman's son. By definition a barren woman has no children.
Somewhat more interesting is the example of the horned hare. I have
heard animated arguments among Tibetans over whether it is an analytic
truth or a synthetic truth that hares have no horns. If anyone settles
that dispute definitively, I'll let you know.

As an aside, here in New Mexico a favorite joke to pull on visitors is
to tell them that somewhere out in the arid foothills there is a huge
jack rabbit that has antlers. It's called a jackalope. Tourists are
advised to keep their eyes open for them. Once when a Tibetan geshe was
visiting New Mexico, his friend bought a statue of a jackalope in a
tourist shop and said "See, Geshe-la, this proves that it's not
impossible for a rabbit to have horns. One can imagine such a thing. If
one can imagine something, it's not a logical impossibility. So it can't
be true by definition that rabbits do not have horns. It's a synthetic
truth." The geshe was unimpressed. He said "That's not a rabbit. If it
were, it would not have horns. It's a jackalope."

-- 
Richard Hayes
Department of Philosophy
University of New Mexico